the topic of this video is electromagnetic energy and specifically line spectra the learning objective here is to distinguish between line and continuous emission spectra so um first we'll talk about a continuous emission spectrum and this a continuous emission spectrum is produced generally from solids liquids and condensed gases and you can think about even the the sun as producing an emission spectrum we looked at a solar output plot in a previous video that showed the sun is emitting a wide range of wavelengths of light and we can you know separate those out into their individual wavelengths using like a prism so taking white light to see a bunch of different colors but but all of the light being emitted by the sun is in a continuous spectrum so a continuous spectrum can be seen on the top of this figure where we see all of the wavelengths of visible light here so this is this is what we would refer to as a continuous spectrum now uh what happens if you if you take um a gas and you put it into a glass tube with electrical contacts on either end of this tube and you pass electricity through the tube of a gas what you get is not a continuous spectrum but a line spectrum so all of these down here are examples of line spectra so spectra ending with um tra is the plural of spectrum okay so here you can see different samples we have sodium line spectrum of sodium line spectrum of hydrogen calcium and mercury in this particular case you notice it's not of all the visible wavelengths of light it's very discrete and every single uh line here it corresponds to one specific wavelength not a not a spread of wavelengths one specific wavelength so this is really interesting because now we can see that in gases if you they emit energy uh in the form of electromagnetic radiation at very discrete energy values not all different types of energies but very very discrete um energy values so the big one that we're going to talk about next is the line spectrum for hydrogen because here it is you know it's it's relatively simple but it's also very it was very um perplexing to physicists in the early 1900s as to why would hydrogen only emit at these very specific energy values so some of the big developments uh regarding this were from a physicist named johann balmer and he came up with a way to mathematically uh model the first four visible wavelengths of light emitted by hydrogen and you'll notice here these are the uh there's one two three four the uh johann balmer was able to to account for those but um i'm going to talk about uh another physicist by the name of johannes rydberg and ribberg came up with an equation that could actually account for all of hydrogen's emissions so his equation is 1 over lambda which is wavelength is equal to capital r and then i'll put that's supposed to be at infinity symbol so this is a constant called the rydberg constant multiplied by 1 over n 1 squared minus 1 over n subscript 2 squared okay so here um r infinity is called the right uh the rydberg constant and that is a value in this particular case of 1.097 times 10 to the 7th per meter and these values here of n 1 and n 2 correspond to whole integer values okay where uh n2 here is um an integer value greater than and one so uh this is a really really uh important um uh equation because it'll it it sort of not only allowed you to predict any emission of light from the hydrogen atom itself but um it used quantized integers to do that these n1 and n2 values and so this is what ultimately helped push forward quantum mechanics as a field to describe the electronic structure of matter